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1 # Comments start with # 2 # The first line of a new text is TitleText 3 # Edition and Author must be there too 4 # Blank lines are only for decoration 5 6 TitleText('Financial Mathematics') 7 EditionText('1') 8 AuthorText('Holt') 9 10 1 >>> Introduction to Interest 11 1.0 >>> Algebra Prerequisites 12 1.1 >>> Simple Interest 13 1.2 >>> Compound Interest 14 1.3 >>> Effective and Nominal Rates of Interest 15 1.4 >>> Present and Future Value 16 17 2 >>> Equations of Value 18 2.1 >>> Time Value of Money 19 2.2 >>> Unknown Time and Logarithms 20 2.3 >>> Dollar Weighted Rate of Return 21 2.4 >>> Time Weighted Rate of Return 22 23 3 >>> Annuities 24 3.1 >>> Geometric Sums 25 3.2 >>> Annuities 26 3.3 >>> Loans 27 3.4 >>> Sinking Funds 28 3.5 >>> Varying Payments 29 3.6 >>> Perpetuities 30 31 4 >>> Bonds 32 4.1 >>> Yield Rates 33 4.2 >>> Bonds 34 4.3 >>> Book Value 35 4.4 >>> Other Bonds 36 37 5 >>> Probability and Contingent Payments 38 5.1 >>> Introduction to Probability 39 5.2 >>> Expected Values 40 5.3 >>> Contingent Payments 41 42 6 >>> Options 43 6.1 >>> Introduction to Options 44 6.2 >>> Hedging Strategies 45 6.3 >>> Binomial Trees 46 47 TitleText('Mathematical Statistics') 48 EditionText('6') 49 AuthorText('Wackerly, Mendenhall, Scheaffer') 50 51 1 >>> What Is Statistics? 52 1.1 >>> Introduction 53 1.2 >>> Characterizing a Set of Measurements: Graphical Methods 54 1.3 >>> Characterizing a Set of Measurements: Numerical Methods 55 1.4 >>> How Inferences Are Made 56 1.5 >>> Theory and Reality 57 1.6 >>> Summary 58 59 2 >>> Probability 60 2.1 >>> Introduction 61 2.2 >>> Probability and Inference 62 2.3 >>> A Review of Set Notation 63 2.4 >>> A Probabilistic Model for an Experiment: The Discrete Case 64 2.5 >>> Calculating the Probability of an Event: The Sample-Point Method 65 2.6 >>> Tools for Counting Sample Points 66 2.7 >>> Conditional Probability and the Independence of Events 67 2.8 >>> Two Laws of Probability 68 2.9 >>> Calculating the Probability of an Event: The Event-Composition Methods 69 2.10 >>> The Law of Total Probability and Bayes's Rule 70 2.11 >>> Numerical Events and Random Variables 71 2.12 >>> Random Sampling 72 2.13 >>> Summary 73 74 3 >>> Discrete Random Variables and Their Probability Distributions 75 3.1 >>> Basic Definition 76 3.2 >>> The Probability Distribution for Discrete Random Variable 77 3.3 >>> The Expected Value of Random Variable or a Function of Random Variable 78 3.4 >>> The Binomial Probability Distribution 79 3.5 >>> The Geometric Probability Distribution 80 3.6 >>> The Negative Binomial Probability Distribution 81 3.7 >>> The Hypergeometric Probability Distribution 82 3.8 >>> Moments and Moment-Generating Functions 83 3.9 >>> Probability-Generating Functions 84 3.10 >>> Tchebysheff's Theorem 85 3.11 >>> Summary 86 87 4 >>> Continuous Random Variables and Their Probability Distributions 88 4.1 >>> Introduction 89 4.2 >>> The Probability Distribution for Continuous Random Variable 90 4.3 >>> The Expected Value for Continuous Random Variable 91 4.4 >>> The Uniform Probability Distribution 92 4.5 >>> The Normal Probability Distribution 93 4.6 >>> The Gamma Probability Distribution 94 4.7 >>> The Beta Probability Distribution 95 4.8 >>> Some General Comments 96 4.9 >>> Other Expected Values 97 4.10 >>> Tchebysheff's Theorem 98 4.11 >>> Expectations of Discontinuous Functions and Mixed Probability Distributions 99 4.12 >>> Summary 100 101 5 >>> Multivariate Probability Distributions 102 5.1 >>> Introduction 103 5.2 >>> Bivariate and Multivariate Probability Distributions 104 5.3 >>> Independent Random Variables 105 5.4 >>> The Expected Value of a Function of Random Variables 106 5.5 >>> Special Theorems 107 5.6 >>> The Covariance of Two Random Variables 108 5.7 >>> The Expected Value and Variance of Linear Functions of Random Variables 109 5.8 >>> The Multinomial Probability Distribution 110 5.9 >>> The Bivariate Normal Distribution 111 5.10 >>> Conditional Expectations 112 5.11 >>> Summary 113 114 6 >>> Functions of Random Variables 115 6.1 >>> Introductions 116 6.2 >>> Finding the Probability Distribution of a Function of Random Variables 117 6.3 >>> The Method of Distribution Functions 118 6.4 >>> The Methods of Transformations 119 6.5 >>> Multivariable Transformations Using Jacobians 120 6.6 >>> Order Statistics 121 6.7 >>> Summary 122 123 7 >>> Sampling Distributions and the Central Limit Theorem 124 7.1 >>> Introduction 125 7.2 >>> Sampling Distributions Related to the Normal Distribution 126 7.3 >>> The Central Limit Theorem 127 7.4 >>> A Proof of the Central Limit Theorem 128 7.5 >>> The Normal Approximation to the Binomial Distributions 129 7.6 >>> Summary 130 131 8 >>> Estimation 132 8.1 >>> Introduction 133 8.2 >>> The Bias and Mean Square Error of Point Estimators 134 8.3 >>> Some Common Unbiased Point Estimators 135 8.4 >>> Evaluating the Goodness of Point Estimator 136 8.5 >>> Confidence Intervals 137 8.6 >>> Large-Sample Confidence Intervals Selecting the Sample Size 138 8.7 >>> Small-Sample Confidence Intervals for u and u1-u2 139 8.8 >>> Confidence Intervals for o2 140 8.9 >>> Summary 141 142 9 >>> Properties of Point Estimators and Methods of Estimation 143 9.1 >>> Introduction 144 9.2 >>> Relative Efficiency 145 9.3 >>> Consistency 146 9.4 >>> Sufficiency 147 9.5 >>> The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation 148 9.6 >>> The Method of Moments 149 9.7 >>> The Method of Maximum Likelihood 150 9.8 >>> Some Large-Sample Properties of MLEs 151 9.9 >>> Summary 152 153 10 >>> Hypothesis Testing 154 10.1 >>> Introduction 155 10.2 >>> Elements of a Statistical Test 156 10.3 >>> Common Large-Sample Tests 157 10.4 >>> Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test 158 10.5 >>> Relationships Between Hypothesis Testing Procedures and Confidence Intervals 159 10.6 >>> Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values 160 10.7 >>> Some Comments on the Theory of Hypothesis Testing 161 10.8 >>> Small-Sample Hypothesis Testing for u and u1-u2 162 10.9 >>> Testing Hypotheses Concerning Variances 163 10.10 >>> Power of Test and the Neyman-Pearson Lemma 164 10.11 >>> Likelihood Ration Test 165 10.12 >>> Summary 166 167 11 >>> Linear Models and Estimation by Least Squares 168 11.1 >>> Introduction 169 11.2 >>> Linear Statistical Models 170 11.3 >>> The Method of Least Squares 171 11.4 >>> Properties of the Least Squares Estimators for the Simple Linear Regression Model 172 11.5 >>> Inference Concerning the Parameters BI 173 11.6 >>> Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression 174 11.7 >>> Predicting a Particular Value of Y Using Simple Linear Regression 175 11.8 >>> Correlation 176 11.9 >>> Some Practical Examples 177 11.10 >>> Fitting the Linear Model by Using Matrices 178 11.11 >>> Properties of the Least Squares Estimators for the Multiple Linear Regression Model 179 11.12 >>> Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression 180 11.13 >>> Prediction a Particular Value of Y Using Multiple Regression 181 11.14 >>> A Test for H0: Bg+1 + Bg+2 = ? = Bk = 0 182 11.15 >>> Summary and Concluding Remarks 183 184 12 >>> Considerations in Designing Experiments 185 12.1 >>> The Elements Affecting the Information in a Sample 186 12.2 >>> Designing Experiment to Increase Accuracy 187 12.3 >>> The Matched Pairs Experiment 188 12.4 >>> Some Elementary Experimental Designs 189 12.5 >>> Summary 190 191 13 >>> The Analysis of Variance 192 13.1 >>> Introduction 193 13.2 >>> The Analysis of Variance Procedure 194 13.3 >>> Comparison of More than Two Means: Analysis of Variance for a One-way Layout 195 13.4 >>> An Analysis of Variance Table for a One-Way Layout 196 13.5 >>> A Statistical Model of the One-Way Layout 197 13.6 >>> Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout 198 13.7 >>> Estimation in the One-Way Layout 199 13.8 >>> A Statistical Model for the Randomized Block Design 200 13.9 >>> The Analysis of Variance for a Randomized Block Design 201 13.10 >>> Estimation in the Randomized Block Design 202 13.11 >>> Selecting the Sample Size 203 13.12 >>> Simultaneous Confidence Intervals for More than One Parameter 204 13.13 >>> Analysis of Variance Using Linear Models 205 13.14 >>> Summary 206 207 14 >>> Analysis of Categorical Data 208 14.1 >>> A Description of the Experiment 209 14.2 >>> The Chi-Square Test 210 14.3 >>> A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test 211 14.4 >>> Contingency Tables 212 14.5 >>> r x c Tables with Fixed Row or Column Totals 213 14.6 >>> Other Applications 214 14.7 >>> Summary and Concluding Remarks 215 216 15 >>> Nonparametric Statistics 217 15.1 >>> Introduction 218 15.2 >>> A General Two-Sampling Shift Model 219 15.3 >>> A Sign Test for a Matched Pairs Experiment 220 15.4 >>> The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment 221 15.5 >>> The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples 222 15.6 >>> The Mann-Whitney U Test: Independent Random Samples 223 15.7 >>> The Kruskal-Wallis Test for One-Way Layout 224 15.8 >>> The Friedman Test for Randomized Block Designs 225 15.9 >>> The Runs Test: A Test for Randomness 226 15.10 >>> Rank Correlation Coefficient 227 15.11 >>> Some General Comments on Nonparametric Statistical Test 228 229 16 >>> Appendix 1: Matrices and Other Useful Mathematical Results 230 16.1 >>> Appendix 1.1: Matrices and Matrix Algebra 231 16.2 >>> Appendix 1.2: Addition of Matrices 232 16.3 >>> Appendix 1.3: Multiplication of a Matrix by a Real Number 233 16.4 >>> Appendix 1.4: Matrix Multiplication 234 16.5 >>> Appendix 1.5: Identity Elements 235 16.6 >>> Appendix 1.6: The Inverse of a Matrix 236 16.7 >>> Appendix 1.7: The Transpose of a Matrix 237 16.8 >>> Appendix 1.8: A Matrix Expression for a System of Simultaneous Linear Equations 238 16.9 >>> Appendix 1.9: Inverting a Matrix 239 16.10 >>> Appendix 1.10: Solving a System of Simultaneous Linear Equations 240 16.11 >>> Appendix 1.11: Other Useful Mathematical Results 241 242 17 >>> Appendix 2: Common Probability Distributions, Means, Variances, and Moment Generating Functions 243 17.1 >>> Appendix 2.1: Discrete Distributions 244 17.2 >>> Appendix 2.2: Continuous Distributions. 245 246 18 >>> Appendix 3: Tables 247 18.1 >>> Appendix 3.1: Binomial Probabilities 248 18.2 >>> Appendix 3.2: Table of e-x 249 18.3 >>> Appendix 3.3: Poisson Probabilities 250 18.4 >>> Appendix 3.4: Normal Curve Areas 251 18.5 >>> Appendix 3.5: Percentage Points of the t Distributions 252 18.6 >>> Appendix 3.6: Percentage Points of the F Distributions 253 18.7 >>> Appendix 3.7: Distribution of Function U 254 18.8 >>> Appendix 3.8: Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test 255 18.9 >>> Appendix 3.9: Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a) 256 18.10 >>> Appendix 3.10: Critical Values of Pearman's Rank Correlation Coefficient 257 18.11 >>> Appendix 3.11: Random Numbers 258 259 TitleText('Calculus') 260 EditionText('5') 261 AuthorText('Stewart') 262 263 1 >>> Functions and Models 264 1.1 >>> Four Ways to Represent a Function 265 1.2 >>> Mathematical Models: A Catalog of Essential Functions 266 1.3 >>> New Functions from Old Functions 267 1.4 >>> Graphing Calculators and Computers 268 269 2 >>> Limits and Rates of Change 270 2.1 >>> The Tangent and Velocity Problems 271 2.2 >>> The Limit of a Function 272 2.3 >>> Calculating Limits Using the Limit Laws 273 2.4 >>> The Precise Definition of a Limit 274 2.5 >>> Continuity 275 2.6 >>> Tangents, Velocities, and Other Rates of Change 276 277 3 >>> Derivatives 278 3.1 >>> Derivatives 279 3.2 >>> The Derivative as a Function 280 3.3 >>> Differentiation Formulas 281 3.4 >>> Rates of Change in the Natural and Social Sciences 282 3.5 >>> Derivatives of Trigonometric Functions 283 3.6 >>> The Chain Rule 284 3.7 >>> Implicit Differentiation 285 3.8 >>> Higher Derivatives 286 3.9 >>> Related Rates 287 3.10 >>> Linear Approximations and Differentials 288 289 4 >>> Applications of Differentiation 290 4.1 >>> Maximum and Minimum Values 291 4.2 >>> The Mean Value Theorem 292 4.3 >>> How Derivatives Affect the Shape of a Graph 293 4.4 >>> Limits at Infinity; Horizontal Asymptotes 294 4.5 >>> Summary of Curve Sketching 295 4.6 >>> Graphing with Calculus and Calculators 296 4.7 >>> Optimization Problems 297 4.8 >>> Applications to Business and Economics 298 4.9 >>> Newton's Method 299 4.10 >>> Antiderivatives 300 301 5 >>> Integrals 302 5.1 >>> Areas and Distances 303 5.2 >>> The Definite Integral 304 5.3 >>> The Fundamental Theorem of Calculus 305 5.4 >>> Indefinite Integrals and the Net Change Theorem 306 5.5 >>> The Substitution Rule 307 308 6 >>> Applications of Integration 309 6.1 >>> Areas between Curves 310 6.2 >>> Volumes 311 6.3 >>> Volumes by Cylindrical Shells 312 6.4 >>> Work 313 6.5 >>> Average Value of a Function 314 315 7 >>> Inverse Functions 316 7.1 >>> Inverse Functions 317 7.2 >>> Exponential Functions and Their Derivatives 318 7.3 >>> Logarithmic Functions 319 7.4 >>> Derivatives of Logarithmic Functions 320 7.5 >>> Inverse Trigonometric Functions 321 7.6 >>> Hyperbolic Functions 322 7.7 >>> Indeterminate Forms and L'Hospital's Rule 323 324 8 >>> Techniques of Integration 325 8.1 >>> Integration by Parts 326 8.2 >>> Trigonometric Integrals 327 8.3 >>> Trigonometric Substitution 328 8.4 >>> Integration of Rational Functions by Partial Fractions 329 8.5 >>> Strategy for Integration 330 8.6 >>> Integration Using Tables and Computer Algebra Systems 331 8.7 >>> Approximate Integration 332 8.8 >>> Improper Integrals 333 334 9 >>> Further Applications of Integration 335 9.1 >>> Arc Length 336 9.2 >>> Area of a Surface of Revolution 337 9.3 >>> Applications to Physics and Engineering 338 9.4 >>> Applications to Economics and Biology 339 9.5 >>> Probability 340 341 10 >>> Differential Equations 342 10.1 >>> Modeling with Differential Equations 343 10.2 >>> Direction Fields and Euler's Method 344 10.3 >>> Separable Equations 345 10.4 >>> Exponential Growth and Decay 346 10.5 >>> The Logistic Equation 347 10.6 >>> Linear Equations 348 10.7 >>> Predator-Prey Systems 349 350 11 >>> Parametric Equations and Polar Coordinates 351 11.1 >>> Curves Defined by Parametric Equations 352 11.2 >>> Calculus with Parametric Curves 353 11.3 >>> Polar Coordinates 354 11.4 >>> Areas and Lengths in Polar Coordinates 355 11.5 >>> Conic Sections 356 11.6 >>> Conic Sections in Polar Coordinates 357 358 12 >>> Infinite Sequences and Series 359 12.1 >>> Sequences 360 12.2 >>> Series 361 12.3 >>> The Integral Test and Estimates of Sums 362 12.4 >>> The Comparison Tests 363 12.5 >>> Alternating Series 364 12.6 >>> Absolute Convergence and the Ratio and Root Tests 365 12.7 >>> Strategy for Testing Series 366 12.8 >>> Power Series 367 12.9 >>> Representations of Functions as Power Series 368 12.10 >>> Taylor and Maclaurin Series 369 12.11 >>> The Binomial Series 370 12.12 >>> Applications of Taylor Polynomials 371 372 13 >>> Vectors and the Geometry of Space 373 13.1 >>> Three-Dimensional Coordinate Systems 374 13.2 >>> Vectors 375 13.3 >>> The Dot Product 376 13.4 >>> The Cross Product 377 13.5 >>> Equations of Lines and Planes 378 13.6 >>> Cylinders and Quadric Surfaces 379 13.7 >>> Cylindrical and Spherical Coordinates 380 381 14 >>> Vector Functions 382 14.1 >>> Vector Functions and Space Curves 383 14.2 >>> Derivatives and Integrals of Vector Functions 384 14.3 >>> Arc Length and Curvature 385 14.4 >>> Motion in Space: Velocity and Acceleration 386 387 15 >>> Partial Derivatives 388 15.1 >>> Functions of Several Variables 389 15.2 >>> Limits and Continuity 390 15.3 >>> Partial Derivatives 391 15.4 >>> Tangent Planes and Linear Approximations 392 15.5 >>> The Chain Rule 393 15.6 >>> Directional Derivatives and the Gradient Vector 394 15.7 >>> Maximum and Minimum Values 395 15.8 >>> Lagrange Multipliers 396 397 16 >>> Multiple Integrals 398 16.1 >>> Double Integrals over Rectangles 399 16.2 >>> Iterated Integrals 400 16.3 >>> Double Integrals over General Regions 401 16.4 >>> Double Integrals in Polar Coordinates 402 16.5 >>> Applications of Double Integrals 403 16.6 >>> Surface Area 404 16.7 >>> Triple Integrals 405 16.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates 406 16.9 >>> Change of Variables in Multiple Integrals 407 408 17 >>> Vector Calculus 409 17.1 >>> Vector Fields 410 17.2 >>> Line Integrals 411 17.3 >>> The Fundamental Theorem for Line Integrals 412 17.4 >>> Green's Theorem 413 17.5 >>> Curl and Divergence 414 17.6 >>> Parametric Surfaces and Their Areas 415 17.7 >>> Surface Integrals 416 17.8 >>> Stokes' Theorem 417 17.9 >>> The Divergence Theorem 418 17.10 >>> Summary 419 420 18 >>> Second-Order Differential Equations 421 18.1 >>> Second-Order Linear Equations 422 18.2 >>> Nonhomogeneous Linear Equations 423 18.3 >>> Applications of Second- Order Differential Equations 424 18.4 >>> Series Solutions 425 426 25 >>> Appendix H: Complex Numbers 427 428 TitleText('College Algebra') 429 EditionText('4') 430 AuthorText('Stewart, Redlin, Watson') 431 432 0 >>> Prerequisites 433 0.1 >>> Modeling the Real World 434 0.2 >>> Real Numbers 435 0.3 >>> Integer Exponents 436 0.4 >>> Rational Exponents and Radicals 437 0.5 >>> Algebraic Expressions 438 0.6 >>> Factoring 439 0.7 >>> Rational Expressions 440 441 1 >>> Equations and Inequalities 442 1.1 >>> Basic Equations 443 1.2 >>> Modeling with Equations 444 1.3 >>> Quadratic Equations 445 1.4 >>> Complex Numbers 446 1.5 >>> Other Types of Equations 447 1.6 >>> Inequalities 448 1.7 >>> Absolute Value Equations and Inequalities 449 450 2 >>> Coordinates and Graphs 451 2.1 >>> The Coordinate Plane 452 2.2 >>> Graphs of Equations in Two Variables 453 2.3 >>> Graphing Calculators; Solving Equations and Inequalitie Graphically 454 2.4 >>> Lines 455 2.5 >>> Modeling: Variation 456 457 3 >>> Functions 458 3.1 >>> What Is a Function? 459 3.2 >>> Graphs of Functions 460 3.3 >>> Increasing and Decreasing Functions; Average Rate of Change 461 3.4 >>> Transformations of Functions 462 3.5 >>> Quadratic Functions; Maxima and Minima 463 3.6 >>> Combining Functions 464 3.7 >>> One-to-One Functions and Their Inverses 465 466 4 >>> Polynomial and Rational Functions 467 4.1 >>> Polynomial Functions and Their Graphs 468 4.2 >>> Dividing Polynomials 469 4.3 >>> Real Zeros of Polynomials 470 4.4 >>> Complex Zeros and the Fundamental Theorem of Algebra 471 4.5 >>> Rational Functions 472 5 >>> Exponential and Logarithmic Functions 473 5.1 >>> Exponential Functions 474 5.2 >>> Logarithmic Functions 475 5.3 >>> Laws of Logarithms 476 5.4 >>> Exponential and Logarithmic Equations 477 5.5 >>> Modeling with Exponential and Logarithmic Functions 478 479 6 >>> Systems of Equations and Inequalities 480 6.1 >>> Systems of Equations 481 6.2 >>> Systems of Linear Equations in Two Variables 482 6.3 >>> Systems of Linear Equations in Several Variables 483 6.4 >>> Systems of Inequalities 484 6.5 >>> Partial Fractions 485 486 7 >>> Matrices and Determinants 487 7.1 >>> Matrices and Systems of Linear Equations 488 7.2 >>> The Algebra of Matrices 489 7.3 >>> Inverses of Matrices and Matrix Equations 490 7.4 >>> Determinants and Cramer's Rule 491 492 8 >>> Conic Sections 493 8.1 >>> Parabolas 494 8.2 >>> Ellipses 495 8.3 >>> Hyperbolas 496 8.4 >>> Shifted Conics 497 498 9 >>> Sequences and Series 499 9.1 >>> Sequences and Summation Notation 500 9.2 >>> Arithmetic Sequences 501 9.3 >>> Geometric Sequences 502 9.4 >>> Mathematics of Finance 503 9.5 >>> Mathematical Induction 504 9.6 >>> The Binomial Theorem 505 506 10 >>> Counting and Probability 507 10.1 >>> Counting Principles 508 10.2 >>> Permutations and Combinations 509 10.3 >>> Probability 510 10.4 >>> Binomial Probability 511 10.5 >>> Expected Value 512 513 TitleText('Statistics for Management and Economics') 514 EditionText('7') 515 AuthorText('Keller') 516 517 1 >>> What is Statistics? 518 1.1 >>> Key Statistical Concepts 519 1.2 >>> Statistical Applications in Business 520 1.3 >>> Statistics and the Computer 521 1.4 >>> World Wide Web and Learning Center 522 1.A >>> Instructions for the CD-ROM 523 1.B >>> Introduction to Microsoft Excel 524 1.C >>> Introduction to Minitab 525 2 >>> Graphical and Tabular Descriptive Techniques 526 2.1 >>> Types of Data and Information 527 2.2 >>> Graphical and Tabular Techniques for Nominal Data 528 2.3 >>> Graphical Techniques for Interval Data 529 2.4 >>> Describing the relationship Between Two Variables 530 2.5 >>> Describing Time-Series Data 531 3 >>> Art and Science of Graphical Presentations 532 3.1 >>> Graphical Excellence 533 3.2 >>> Graphical Deception 534 3.3 >>> Presenting Statistics: Written Reports and Oral Presentations 535 4 >>> Numerical Descriptive Techniques 536 4.1 >>> Measures of Central Location 537 4.2 >>> Measures of Variability 538 4.3 >>> Measures of Relative Standing and Box Plots 539 4.4 >>> Measures of Linear Relationship 540 4.5 >>> Applications in Professional Sports: Baseball 541 4.6 >>> Comparing Graphical and Numerical Techniques 542 4.7 >>> General Guidelines for Exploring Data 543 5 >>> Data Collection and Sampling 544 5.1 >>> Methods of Collecting Data 545 5.2 >>> Sampling 546 5.3 >>> Sampling Plans 547 5.4 >>> Sampling and Nonsampling Errors 548 6 >>> Probability 549 6.1 >>> Assigning Probability to Events 550 6.2 >>> Joint, Marginal, and Conditional Probability 551 6.3 >>> Probability Rules and Trees 552 6.4 >>> Bayes' Law 553 6.5 >>> Identifying the Correct Method 554 7 >>> Random Variables and Discrete Probability Distributions 555 7.1 >>> Random Variables and Probability Distributions 556 7.2 >>> Bivariate Distributions 557 7.3 >>> Applications in Finance: Portfolio Diversification and Asset Allocation 558 7.4 >>> Binomial Distribution 559 7.5 >>> Poisson Distribution 560 8 >>> Continuous Probability Distributions 561 8.1 >>> Probability Density Functions 562 8.2 >>> Normal Distribution 563 8.3 >>> Exponential Distribution 564 8.4 >>> Other Continuous Distributions 565 9 >>> Sampling Distributions 566 9.1 >>> Sampling Distribution of the Mean 567 9.2 >>> Sampling Distribution of a Proportion 568 9.3 >>> Sampling Distribution of the Difference Between Two Means 569 9.4 >>> From Here to Inference 570 10 >>> Introduction to Estimation 571 10.1 >>> Concepts of Estimation 572 10.2 >>> Estimating the Population Mean When the Population Standard Deviation is Known 573 10.3 >>> Selecting the Sample Size 574 11 >>> Introduction to Hypothesis Testing 575 11.1 >>> Concepts of Hypothesis Testing 576 11.2 >>> Testing the Population Mean When the Population Standard Deviation is Known 577 11.3 >>> Calculating the Probability of a Type II Error 578 11.4 >>> The Road Ahead 579 12 >>> Inference About a Population 580 12.1 >>> Inference About a Population Mean When the Standard Deviation is Unknown 581 12.2 >>> Inference about a Population Variance 582 12.3 >>> inference about a Population Proportion 583 12.4 >>> Applications in Marketing: Market Segmentation 584 12.5 >>> Applications in Marketing: Auditing 585 13 >>> Inference About Comparing Two Populations 586 13.1 >>> Inference about the Difference Between Two Means: Independent Samples 587 13.2 >>> Observational and Experimental Data 588 13.3 >>> Inference about the Difference Between Two Means: Matched Pairs Experiment 589 13.4 >>> Inference about the Ratio of Two Variances 590 13.5 >>> Inference about the Difference Between Two Population Proportions 591 13.A >>> Excel Instructions for Stacked and Unstacked Data 592 13.B >>> Minitab Instructions for Stacked and Unstacked Data 593 14 >>> Statistical Inference: Review of Chapters 12 and 13 594 14.1 >>> Guide to Identifying the Correct Technique: Chapters 12 and 13 595 15 >>> Analysis of Variance 596 15.1 >>> One-Way Analysis of Variance 597 15.2 >>> Analysis of Variance Experimental Designs 598 15.3 >>> Randomized Blocks (Two-Way) Analysis of Variance 599 15.4 >>> Two-Factor Analysis of Variance 600 15.5 >>> Appplications in Operations Management: Finding and Reducing Variation 601 15.6 >>> Multiple Comparisons 602 16 >>> Chi-Squared Tests 603 16.1 >>> Chi-Squared Goodness-of-Fit Test 604 16.2 >>> Chi-Squared Test of a Contingency Table 605 16.3 >>> Summary of Tests on Nominal Data 606 16.4 >>> Chi-Squared Tests of Normality 607 17 >>> Simple Linear Regression and Correlation 608 17.1 >>> Model 609 17.2 >>> Estimating the Coefficients 610 17.3 >>> Error Variable: Required Conditions 611 17.4 >>> Assessing the Model 612 17.5 >>> Applications in Finance: Market Model 613 17.6 >>> Using the Regression Equation 614 17.7 >>> Regression Diagnostics-I 615 18 >>> Multiple Regression 616 18.1 >>> Model and Required Conditions 617 18.2 >>> Estimating the Coefficients and Assessing the Model 618 18.3 >>> Regression Diagnostics-II 619 18.4 >>> Regression Diagnostics-III (Time Series) 620 621 19 >>> Appendix A: Excel Troubleshooting and Detailed Instructions 622 20 >>> Appendix B: Minitab Detailed Instructions 623 21 >>> Appendix C: Approximating Means and Variances from Grouped Data 624 22 >>> Appendix D: Descriptive Techniques Review Exercises 625 23 >>> Appendix E: Couting Formulas 626 24 >>> Appendix F: Hypergeometric Distribution 627 25 >>> Appendix G: Continuous Probability Distributions: Calculus Approach 628 26 >>> Appendix H: Using the Laws of Expected Value and Variance to Derive the Parameters of Sampling Distributions 629 27 >>> Appendix I: Excel Spreadsheets for Techniques in Chapters 10-13 630 28 >>> Appendix K: Converting Excel's Probabilities to p-Values 631 29 >>> Appendix J: Excel and Minitab Instructions for Missing Data and for Recoding Data 632 30 >>> Appendix L: Probability of a Type II Error When Testing a Proportion 633 31 >>> Appendix M: Approximating p-Values from the Student t Table 634 32 >>> Appendix N: Probability of a Type II Error When Testing the Difference Between Two Means 635 33 >>> Appendix O: Probability of a Type II Erorr When Testing the Difference Between Two Proportions 636 34 >>> Appendix P: Bartlett's Test 637 35 >>> Appendix Q: Minitab Instructions for the Chi-Squared Goodness-of-Fit Test and the Test for Normality 638 36 >>> Appendix R: The Rule of Five 639 37 >>> Appendix S: Deriving the Normal Equations 640 38 >>> Appendix T: Szroeter's Test for Heteroscedasticity 641 39 >>> Appendix U: Transformations 642 643 TitleText('Elementary Linear Algebra') 644 645 EditionText('5') 646 647 AuthorText('Larson, Edwards, Falvo') 648 649 650 1 >>> Systems of Linear Equations 651 1.1 >>> Introduction to Systems of Linear Equations 652 1.2 >>> Gaussian Elimination and Gauss-Jordan Elimination 653 1.3 >>> Applications of Systems of Linear Equations 654 655 2 >>> Matrices 656 2.1 >>> Operations with Matrices 657 2.2 >>> Properties of Matrix Operations 658 2.3 >>> The Inverse of a Matrix 659 2.4 >>> Elementary Matrices 660 2.5 >>> Applications of Matrix Operations 661 662 3 >>> Determinants 663 3.1 >>> The Determinant of a Matrix 664 3.2 >>> Evaluation of a Determinant Using Elementary Operations 665 3.3 >>> Properties of Determinants 666 3.4 >>> Introduction to Eigenvalues 667 3.5 >>> Applications of Determinants 668 669 4 >>> Vector Spaces 670 671 4.1 >>> Vectors in Rn 672 4.2 >>> Vector Spaces 673 4.3 >>> Subspaces of Vector Spaces 674 4.4 >>> Spanning Sets and Linear Independence 675 4.5 >>> Basis and Dimension 676 4.6 >>> Rank of a Matrix and Systems of Linear Equations 677 4.7 >>> Coordinates and Change of Basis 678 4.8 >>> Applications of Vector Spaces 679 680 5 >>> Inner Product Spaces 681 5.1 >>> Length and Dot Product in Rn 682 5.2 >>> Inner Product Spaces 683 5.3 >>> Orthonormal Bases: Gram-Schmidt Process 684 5.4 >>> Mathematical Models and Least Squares Analysis 685 5.5 >>> Applications of Inner Product Spaces 686 687 6 >>> Linear Transformations 688 6.1 >>> Introduction to Linear Transformations 689 6.2 >>> The Kernel and Range of a Linear Transformation 690 6.3 >>> Matrices for Linear Transformations 691 6.4 >>> Transition Matrices and Similarity 692 6.5 >>> Applications of Linear Transformations 693 694 7 >>> Eigenvalues and Eigenvectors 695 7.1 >>> Eigenvalues and Eigenvectors 696 7.2 >>> Diagonalization 697 7.3 >>> Symmetric Matrices and Orthogonal Diagonalization 698 7.4 >>> Applications of Eigenvalues and Eigenvectors 699 700 8 >>> Complex Vector Spaces 701 8.1 >>> Complex Numbers 702 8.2 >>> Conjugates and Division of Complex Numbers 703 8.3 >>> Polar Form and DeMoivre's Theorem 704 8.4 >>> Complex Vector Spaces and Inner Products 705 8.5 >>> Unitary and Hermitian Matrices 706 707 9 >>> Linear Programming 708 9.1 >>> Systems of Linear Inequalities 709 9.2 >>> Linear Programming Involving Two Variables 710 9.3 >>> The Simplex Method: Maximization 711 9.4 >>> The Simplex Method: Minimization 712 9.5 >>> The Simplex Method: Mixed Constraints 713 714 10 >>> Numerical Methods 715 716 10.1 >>> Gaussian Elimination with Partial Pivoting 717 10.2 >>> Interative Methods for Solving Linear Systems 718 10.3 >>> Power Method for Approximating Eigenvalues 719 10.4 >>> Applications of Numerical Methods 720 721 11 >>> Appendix A: Mathematical Induction and Other Forms of Proofs 722 723 12 >>> Appendix B: Computer Algebra Systems and Graphing Calculators 724 725 TitleText('Basic Multivariable Calculus') 726 EditionText('3') 727 AuthorText('Marsden, Tromba, Weinstein') 728 729 1 >>> Algebra and Geometry of Euclidean Space 730 1.1 >>> Vectors in the Plane and Space 731 1.2 >>> The Inner Product and Distance 732 1.3 >>> 2 x 2 and 3 x 3 Matrices and Determinants 733 1.4 >>> The Cross Product and Planes 734 1.5 >>> n-Dimensional Euclidean Space 735 1.6 >>> Curves in the Plane and in Space 736 737 2 >>> Differentiation 738 2.1 >>> Graphs and Level Surfaces 739 2.2 >>> Partial Derivatives and Continuity 740 2.3 >>> Differentiability, the Derivative Matrix, and Tangent Planes 741 2.4 >>> The Chain Rule 742 2.5 >>> Gradients and Directional Derivatives 743 2.6 >>> Implicit Differentiation 744 745 3 >>> Higher Derivatives and Extrema 746 3.1 >>> Higher Order Partial Derivatives 747 3.2 >>> Taylor's Theorem 748 3.3 >>> Maxima and Minima 749 3.4 >>> Second Derivative Test 750 3.5 >>> Constrained Extrema and Lagrange Multipliers 751 752 4 >>> Vector-Valued Functions 753 4.1 >>> Acceleration 754 4.2 >>> Arc Length 755 4.3 >>> Vector Fields 756 4.4 >>> Divergence and Curl 757 758 5 >>> Multiple Integrals 759 5.1 >>> Volume and Cavalieri's Principle 760 5.2 >>> The Double Integral Over a Rectangle 761 5.3 >>> The Double Integral Over Regions 762 5.4 >>> Triple Integrals 763 5.5 >>> Change of Variables, Cylindrical and Spherical Coordinates 764 5.6 >>> Applications of Multiple Integrals 765 766 6 >>> Integrals Over Curves and Surfaces 767 6.1 >>> Line Integrals 768 6.2 >>> Parametrized Surfaces 769 6.3 >>> Area of a Surface 770 6.4 >>> Surface Integrals 771 772 7 >>> The Integral Theorems of Vector Analysis 773 7.1 >>> Green's Theorem 774 7.2 >>> Stokes' Theorem 775 7.3 >>> Gauss' Theorem 776 7.4 >>> Path Independence and the Fundamental Theorems of Calculus 777 778 TitleText('Precalculus') 779 EditionText('5') 780 AuthorText('Stewart, Redlin, Watson') 781 782 1 >>> Fundamentals 783 1.1 >>> Real Numbers 784 1.2 >>> Exponents and Radicals 785 1.3 >>> Algebraic Expressions 786 1.4 >>> Rational Expression 787 1.5 >>> Equations 788 1.6 >>> Modeling with Equations 789 1.7 >>> Inequalities 790 1.8 >>> Coordinate Geometry 791 1.9 >>> Graphing Calculators; Solving Equations and Inequalities Graphically 792 1.10 >>> Lines 793 1.11 >>> Modeling Variation 794 795 2 >>> Functions 796 2.1 >>> What is a Function? 797 2.2 >>> Graphs of Functions 798 2.3 >>> Increasing and Decreasing Functions; Average Rate of Change 799 2.4 >>> Transformations of Functions 800 2.5 >>> Quadratic Functions; Maxima and Minima 801 2.6 >>> Modeling with Functions 802 2.7 >>> Combining Functions 803 2.8 >>> One-to-One Functions and Their Inverses 804 805 3 >>> Polynomial and Rational Functions 806 3.1 >>> Polynomial Functions and Their Graphs 807 3.2 >>> Dividing Polynomials 808 3.3 >>> Real Zeros of Polynomials 809 3.4 >>> Complex Numbers 810 3.5 >>> Complex Zeros and the Fundamental Theorem of Algebra 811 3.6 >>> Rational Functions 812 813 4 >>> Exponential and Logarithmic Functions 814 4.1 >>> Exponential Functions 815 4.2 >>> Logarithmic Functions 816 4.3 >>> Laws of Logarithms 817 4.4 >>> Exponential and Logarithmic Equations 818 4.5 >>> Modeling with Exponential and Logarithmic Functions 819 820 5 >>> Trigonometric Functions of Real Numbers 821 5.1 >>> The Unit Circle 822 5.2 >>> Trigonometric Functions of Real Numbers 823 5.3 >>> Trigonometric Graphs 824 5.4 >>> More Trigonometric Graphs 825 5.5 >>> Modeling Harmonic Motion 826 827 6 >>> Trigonometric Functions of Angles 828 6.1 >>> Angle Measures 829 6.2 >>> Trigonometry of Right Triangles 830 6.3 >>> Trigonometric Functions of Angles 831 6.4 >>> The Law of Sines 832 6.5 >>> The Law of Cosines 833 834 7 >>> Analytic Trigonometry 835 7.1 >>> Trigonometric Identities 836 7.2 >>> Addition and Subtraction Formulas 837 7.3 >>> Double-Angle, Half-Angle, and Sum-Product Formulas 838 7.4 >>> Inverse Trigonometric Functions 839 7.5 >>> Trigonometric Equations 840 841 8 >>> Polar Coordinates and Vectors 842 8.1 >>> Polar Coordinates 843 8.2 >>> Graphs of Polar Equations 844 8.3 >>> Polar Form of Complex Numbers; DeMoivre's Theorem 845 8.4 >>> Vectors 846 8.5 >>> The Dot Product 847 848 9 >>> Systems of Equations and Inequalities 849 9.1 >>> Systems of Equations 850 9.2 >>> Systems of Linear Equations in Two Variables 851 9.3 >>> Systems of Linear Equations in Several Variables 852 9.4 >>> Systems of Linear Equations: Matrices 853 9.5 >>> The Algebra of Matrices 854 9.6 >>> Inverses of Matrices and Matrix Equations 855 9.7 >>> Determinants and Cramer's Rule 856 9.8 >>> Partial Fractions 857 9.9 >>> Systems of Inequalities 858 859 10 >>> Analytic Geometry 860 10.1 >>> Parabolas 861 10.2 >>> Ellipses 862 10.3 >>> Hyperbolas 863 10.4 >>> Shifted Conics 864 10.5 >>> Rotation of Axes 865 10.6 >>> Polar Equations of Conics 866 10.7 >>> Plane Curves and Parametric Equations 867 868 11 >>> Sequences and Series 869 11.1 >>> Sequences and Summation Notation 870 11.2 >>> Arithmetic Sequences 871 11.3 >>> Geometric Sequences 872 11.4 >>> Mathematics of Finance 873 11.5 >>> Mathematical Induction 874 11.6 >>> The Binomial Theorem 875 876 12 >>> Limits: A Preview of Calculus 877 12.1 >>> Finding Limits Numerically and Graphically 878 12.2 >>> Finding Limits Algebraically 879 12.3 >>> Tangent Lines and Derivatives 880 12.4 >>> Limits at Infinity: Limits of Sequences 881 12.5 >>> Areas 882 883 TitleText('Discrete Mathematics') 884 EditionText('4') 885 AuthorText('Rosen') 886 887 888 1 >>> The Foundations: Logic, Sets, and Functions 889 1.1 >>> Logic 890 1.2 >>> Propositional Equivalences 891 1.3 >>> Predicates and Quantifiers 892 1.4 >>> Sets 893 1.5 >>> Set Operations 894 1.6 >>> Functions 895 1.7 >>> Sequences and Summations 896 1.8 >>> The Growth Functions 897 898 2 >>> The Fundamentals: Algorithms, the Integers, and Matrices 899 2.1 >>> Algorithms 900 2.2 >>> Complexity of Algorithms 901 2.3 >>> The Integers and Division 902 2.4 >>> Integers and Algorithms 903 2.5 >>> Applications of Number Theory 904 2.6 >>> Matrices 905 906 3 >>> Mathematical Reasoning 907 908 3.1 >>> Methods of Proof 909 3.2 >>> Mathematical Induction 910 3.3 >>> Recursive Definitions 911 3.4 >>> Recursive Algorithms 912 3.5 >>> Program Correctness 913 914 4 >>> Counting 915 4.1 >>> The Basics of Counting 916 4.2 >>> The Pigeonhole Principle 917 4.3 >>> Permutations and Combinations 918 4.4 >>> Discrete Probability 919 4.5 >>> Probability Theory 920 4.6 >>> Generalized Permutations and Combinations 921 4.7 >>> Generating Permutations and Combinations 922 923 5 >>> Advanced Counting Techniques 924 5.1 >>> Recurrence Relations 925 5.2 >>> Solving Recurrence Relations 926 5.3 >>> Divide-and-Conquer Relations 927 5.4 >>> Generating Functions 928 5.5 >>> Inclusion-Exclusion 929 5.6 >>> Applications of Inclusion-Exclusion 930 931 6 >>> Relations 932 6.1 >>> Relations and Their Properties 933 6.2 >>> n-ary Relations and Their Applications 934 6.3 >>> Representing Relations 935 6.4 >>> Closures of Relations 936 6.5 >>> Equivalence Relations 937 6.6 >>> Partial Orderings 938 939 7 >>> Graphs 940 7.1 >>> Introduction to Graphs 941 7.2 >>> Graph Terminology 942 7.3 >>> Representing Graphs and Graph Isomorphism 943 7.4 >>> Connectivity 944 7.5 >>> Euler and Hamilton Paths 945 7.6 >>> Shortest Path Problems 946 7.7 >>> Planar Graphs 947 7.8 >>> Graph Coloring 948 949 8 >>> Trees 950 8.1 >>> Introduction to Trees 951 8.2 >>> Applications of Trees 952 8.3 >>> Tree Traversal 953 8.4 >>> Trees and Sorting 954 8.5 >>> Spanning Trees 955 8.6 >>> Minimum Spanning Trees 956 957 9 >>> Boolean Algebra 958 9.1 >>> Boolean Functions 959 9.2 >>> Representing Boolean Functions 960 9.3 >>> Logic Gates 961 9.4 >>> Minimization of Circuits 962 963 10 >>> Modeling Computation 964 10.1 >>> Languages and Grammars 965 10.2 >>> Finite-State Machines with Output 966 10.3 >>> Finite-State Machines with No Output 967 10.4 >>> Language Recognition 968 10.5 >>> Turing Machines 969 970 11 >>> Appendix: Exponential and Logarithmic Functions 971 12 >>> Appendix: Pseudocode 972 973 TitleText('Complex Analysis') 974 EditionText('3') 975 AuthorText('Saff, Snider') 976 977 1 >>> Complex Numbers 978 1.1 >>> The Algebra of Complex Numbers 979 1.2 >>> Point Representation of Complex Numbers 980 1.3 >>> Vectors and Polar Forms 981 1.4 >>> The Complex Exponential 982 1.5 >>> Powers and Roots 983 1.6 >>> Planar Sets 984 1.7 >>> The Riemann Sphere and Stereographic Projection 985 986 2 >>> Analytic Functions 987 2.1 >>> Functions of a Complex Variable 988 2.2 >>> Limits and Continuity 989 2.3 >>> Analyticity 990 2.4 >>> The Cauchy-Riemann Equations 991 2.5 >>> Harmonic Functions 992 2.6 >>> Steady-State Temperature as a Harmonic Function 993 2.7 >>> Iterated Maps: Julia and Mandelbrot Sets 994 995 3 >>> Elementary Functions 996 3.1 >>> Polynomials and Rational Functions 997 3.2 >>> The Exponential, Trigonometric, and Hyperbolic Functions 998 3.3 >>> The Logarithmic Function 999 3.4 >>> Washers, Wedges, and Walls 1000 3.5 >>> Complex Powers and Inverse Trigonometric Functions 1001 3.6 >>> Application to Oscillating Systems 1002 1003 4 >>> Complex Integration 1004 4.1 >>> Contours 1005 4.2 >>> Contour Integrals 1006 4.3 >>> Independence of Path 1007 4.4 >>> Cauchy's Integral Theorem 1008 4.5 >>> Deformation of Contours Approach 1009 4.6 >>> Vector Analysis Approach 1010 4.7 >>> Cauchy's Integral Formula and Its Consequences 1011 4.8 >>> Bounds for Analytic Functions 1012 4.9 >>> Applications to Harmonic Functions 1013 1014 5 >>> Series Representations for Analytic Functions 1015 5.1 >>> Sequences and Series 1016 5.2 >>> Taylor Series 1017 5.3 >>> Power Series 1018 5.4 >>> Mathematical Theory of Convergence 1019 5.5 >>> Laurent Series 1020 5.6 >>> Zeros and Singularities 1021 5.7 >>> The Point at Infinity 1022 5.8 >>> Analytic Continuation 1023 1024 6 >>> Residue Theory 1025 6.1 >>> The Residue Theorem 1026 6.2 >>> Trigonometric Integrals over [0, 2¹] 1027 6.3 >>> Improper Integrals of Certain Functions over (--°, °) 1028 6.4 >>> Improper Integrals Involving Trigonometric Functions 1029 6.5 >>> Indented Contours 1030 6.6 >>> Integrals Involving Multiple-Valued Functions 1031 6.7 >>> The Argument Principle and Rouche's Theorem 1032 1033 7 >>> Conformal Mapping 1034 7.1 >>> Invariance of Laplace's Equation 1035 7.2 >>> Geometric Considerations 1036 7.3 >>> Mobius Transformations 1037 7.4 >>> Mobius Transformations, Continued 1038 7.5 >>> The Schwarz-Christoffel Transformation 1039 7.6 >>> Applications in Electrostatics, Heat Flow, and Fluid Mechanics 1040 7.7 >>> Further Physical Applications of Conformal Mapping 1041 1042 8 >>> The Transforms of Applied Mathematics 1043 8.1 >>> Fourier Series (The Finite Fourier Transform) 1044 8.2 >>> The Fourier Transform 1045 8.3 >>> The Laplace Transform 1046 8.4 >>> The z-Transform 1047 8.5 >>> Cauchy Integrals and the Hilbert Transform 1048 1049 9 >>> Appendix A: Numerical Construction of Conformal Maps 1050 9.1 >>> The Schwarz-Christoffel Parameter Problem 1051 9.2 >>> Examples 1052 9.3 >>> Numerical Integration 1053 9.4 >>> Conformal Mapping of Smooth Domains 1054 9.5 >>> Conformal Mapping Software 1055 1056 10 >>> Appendix B: Table of Conformal Mappings 1057 10.1 >>> Mobius Transformations 1058 10.2 >>> Other Transformations 1059 1060 TitleText('Calculus: Early Transcendentals') 1061 EditionText('5') 1062 AuthorText('Stewart') 1063 1064 1 >>> Functions and Models 1065 1.1 >>> Four Ways to Represent a Function 1066 1.2 >>> Mathematical Models: A Catalog of Essential Functions 1067 1.3 >>> New Functions from Old Functions 1068 1.4 >>> Graphing Calculators and Computers 1069 1.5 >>> Exponential Functions 1070 1.6 >>> Inverse Functions and Logarithms 1071 1072 2 >>> Limits and Derivatives 1073 2.1 >>> The Tangent and Velocity Problems 1074 2.2 >>> The Limit of a Function 1075 2.3 >>> Calculating Limits Using the Limit Laws 1076 2.4 >>> The Precise Definition of a Limit 1077 2.5 >>> Continuity 1078 2.6 >>> Limits at Infinity; Horizontal Asymptotes 1079 2.7 >>> Tangents, Velocities, and Other Rates of Change 1080 2.8 >>> Derivatives 1081 2.9 >>> The Derivative as a Function 1082 1083 3 >>> Differentiation Rules 1084 3.1 >>> Derivatives of Polynomials and Exponential Functions 1085 3.2 >>> The Product and Quotient Rules 1086 3.3 >>> Rates of Change in the Natural and Social Sciences 1087 3.4 >>> Derivatives of Trigonometric Functions 1088 3.5 >>> The Chain Rule 1089 3.6 >>> Implicit Differentiation 1090 3.7 >>> Higher Derivatives 1091 3.8 >>> Derivatives of Logarithmic Functions 1092 3.9 >>> Hyperbolic Functions 1093 3.10 >>> Related Rates 1094 3.11 >>> Linear Approximations and Differentials 1095 1096 4 >>> Applications of Differentiation 1097 4.1 >>> Maximum and Minimum Values 1098 4.2 >>> The Mean Value Theorem 1099 4.3 >>> How Derivatives Affect the Shape of a Graph 1100 4.4 >>> Indeterminate Forms and L'Hospital's Rule 1101 4.5 >>> Summary of Curve Sketching 1102 4.6 >>> Graphing with Calculus and Calculators 1103 4.7 >>> Optimization Problems 1104 4.8 >>> Applications to Business and Economics 1105 4.9 >>> Newton's Method 1106 4.10 >>> Antiderivatives 1107 1108 5 >>> Integrals 1109 5.1 >>> Areas and Distances 1110 5.2 >>> The Definite Integral 1111 5.3 >>> The Fundamental Theorem of Calculus 1112 5.4 >>> Indefinite Integrals and the Net Change Theorem 1113 5.5 >>> The Substitution Rule 1114 5.6 >>> The Logarithm Defined as an Integral 1115 1116 6 >>> Applications of Integration 1117 6.1 >>> Areas between Curves 1118 6.2 >>> Volumes 1119 6.3 >>> Volumes by Cylindrical Shells 1120 6.4 >>> Work 1121 6.5 >>> Average Value of a Function 1122 1123 7 >>> Techniques of Integration 1124 7.1 >>> Integration by Parts 1125 7.2 >>> Trigonometric Integrals 1126 7.3 >>> Trigonometric Substitution 1127 7.4 >>> Integration of Rational Functions by Partial Fractions 1128 7.5 >>> Strategy for Integration 1129 7.6 >>> Integration Using Tables and Computer Algebra Systems 1130 7.7 >>> Approximate Integration 1131 7.8 >>> Improper Integrals 1132 1133 8 >>> Further Applications of Integration 1134 8.1 >>> Arc Length 1135 8.2 >>> Area of a Surface of Revolution 1136 8.3 >>> Applications to Physics and Engineering 1137 8.4 >>> Applications to Economics and Biology 1138 8.5 >>> Probability 1139 1140 9 >>> Differential Equations 1141 9.1 >>> Modeling with Differential Equations 1142 9.2 >>> Direction Fields and Euler's Method 1143 9.3 >>> Separable Equations 1144 9.4 >>> Exponential Growth and Decay 1145 9.5 >>> The Logistic Equation 1146 9.6 >>> Linear Equations 1147 9.7 >>> Predator-Prey Systems 1148 1149 10 >>> Parametric Equations and Polar Coordinates 1150 10.1 >>> Curves Defined by Parametric Equations 1151 10.2 >>> Calculus with Parametric Curves 1152 10.3 >>> Polar Coordinates 1153 10.4 >>> Areas and Lengths in Polar Coordinates 1154 10.5 >>> Conic Sections 1155 10.6 >>> Conic Sections in Polar Coordinates 1156 1157 11 >>> Infinite Sequences and Series 1158 11.1 >>> Sequences 1159 11.2 >>> Series 1160 11.3 >>> The Integral Test and Estimates of Sums 1161 11.4 >>> The Comparison Tests 1162 11.5 >>> Alternating Series 1163 11.6 >>> Absolute Convergence and the Ratio and Root Tests 1164 11.7 >>> Strategy for Testing Series 1165 11.8 >>> Power Series 1166 11.9 >>> Representations of Functions as Power Series 1167 11.10 >>> Taylor and Maclaurin Series 1168 11.11 >>> The Binomial Series 1169 11.12 >>> Applications of Taylor Polynomials 1170 1171 12 >>> Vectors and the Geometry of Space 1172 12.1 >>> Three-Dimensional Coordinate Systems 1173 12.2 >>> Vectors 1174 12.3 >>> The Dot Product 1175 12.4 >>> The Cross Product 1176 12.5 >>> Equations of Lines and Planes 1177 12.6 >>> Cylinders and Quadric Surfaces 1178 12.7 >>> Cylindrical and Spherical Coordinates 1179 1180 13 >>> Vector Functions 1181 13.1 >>> Vector Functions and Space Curves 1182 13.2 >>> Derivatives and Integrals of Vector Functions 1183 13.3 >>> Arc Length and Curvature 1184 13.4 >>> Motion in Space: Velocity and Acceleration 1185 1186 14 >>> Partial Derivatives 1187 14.1 >>> Functions of Several Variables 1188 14.2 >>> Limits and Continuity 1189 14.3 >>> Partial Derivatives 1190 14.4 >>> Tangent Planes and Linear Approximations 1191 14.5 >>> The Chain Rule 1192 14.6 >>> Directional Derivatives and the Gradient Vector 1193 14.7 >>> Maximum and Minimum Values 1194 14.8 >>> Lagrange Multipliers 1195 1196 15 >>> Multiple Integrals 1197 15.1 >>> Double Integrals over Rectangles 1198 15.2 >>> Iterated Integrals 1199 15.3 >>> Double Integrals over General Regions 1200 15.4 >>> Double Integrals in Polar Coordinates 1201 15.5 >>> Applications of Double Integrals 1202 15.6 >>> Surface Area 1203 15.7 >>> Triple Integrals 1204 15.8 >>> Triple Integrals in Cylindrical and Spherical Coordinates 1205 15.9 >>> Change of Variables in Multiple Integrals 1206 1207 16 >>> Vector Calculus 1208 16.1 >>> Vector Fields 1209 16.2 >>> Line Integrals 1210 16.3 >>> The Fundamental Theorem for Line Integrals 1211 16.4 >>> Green's Theorem 1212 16.5 >>> Curl and Divergence 1213 16.6 >>> Parametric Surfaces and their Areas 1214 16.7 >>> Surface Integrals 1215 16.8 >>> Stokes' Theorem 1216 16.9 >>> The Divergence Theorem 1217 16.10 >>> Summary 1218 1219 17 >>> Second-Order Differential Equations 1220 17.1 >>> Second-Order Linear Equations 1221 17.2 >>> Nonhomogeneous Linear Equations 1222 17.3 >>> Applications of Second-Order Differential Equations 1223 17.4 >>> Series Solutions 1224 1225 18 >>> Appendix A: Numbers, Inequalities, and Absolute Values 1226 19 >>> Appendix B: Coordinate Geometry and Lines 1227 20 >>> Appendix C: Graphs of Second-Degree Equations 1228 21 >>> Appendix D: Trigonometry 1229 22 >>> Appendix E: Sigma Notation 1230 23 >>> Appendix F: Proofs of Theorems 1231 24 >>> Appendix G: Complex Numbers 1232 25 >>> Appendix H: Answers to Odd-Numbered Exercises 1233 1234 1235 TitleText('Calculus: Early Transcendentals') 1236 EditionText('6') 1237 AuthorText('Stewart') 1238 1239 1 >>> Functions and Models 1240 1.1 >>> Four Ways to Represent a Function 1241 1.2 >>> Mathematical Models: A Catalog of Essential Functions 1242 1.3 >>> New Functions from Old Functions 1243 1.4 >>> Graphing Calculators and Computers 1244 1.5 >>> Exponential Functions 1245 1.6 >>> Inverse Functions and Logarithms 1246 1247 2 >>> Limits and Derivatives 1248 2.1 >>> The Tangent and Velocity Problems 1249 2.2 >>> The Limit of a Function 1250 2.3 >>> Calculating Limits Using the Limit Laws 1251 2.4 >>> The Precise Definition of a Limit 1252 2.5 >>> Continuity 1253 2.6 >>> Limits at Infinity; Horizontal Asymptotes 1254 2.7 >>> Derivatives and Rates of Change 1255 2.8 >>> The Derivative as a Function 1256 1257 3 >>> Differentiation Rules 1258 3.1 >>> Derivatives of Polynomials and Exponential Functions 1259 3.2 >>> The Product and Quotient Rules 1260 3.3 >>> Derivatives of Trigonometric Functions 1261 3.4 >>> The Chain Rule 1262 3.5 >>> Implicit Differentiation 1263 3.6 >>> Derivatives of Logarithmic Functions 1264 3.7 >>> Rates of Change in the Natural and Social Sciences 1265 3.8 >>> Exponential Growth and Decay 1266 3.9 >>> Related Rates 1267 3.10 >>> Linear Approximations and Differentials 1268 3.11 >>> Hyperbolic Functions 1269 1270 4 >>> Applications of Differentiation 1271 4.1 >>> Maximum and Minimum Values 1272 4.2 >>> The Mean Value Theorem 1273 4.3 >>> How Derivatives Affect the Shape of a Graph 1274 4.4 >>> Indeterminate Forms and L'Hospital's Rule 1275 4.5 >>> Summary of Curve Sketching 1276 4.6 >>> Graphing with Calculus and Calculators 1277 4.7 >>> Optimization Problems 1278 4.8 >>> Newton's Method 1279 4.9 >>> Antiderivatives 1280 1281 5 >>> Integrals 1282 5.1 >>> Areas and Distances 1283 5.2 >>> The Definite Integral 1284 5.3 >>> The Fundamental Theorem of Calculus 1285 5.4 >>> Indefinite Integrals and the Net Change Theorem 1286 5.5 >>> The Substitution Rule 1287 1288 6 >>> Applications of Integration 1289 6.1 >>> Areas between Curves 1290 6.2 >>> Volumes 1291 6.3 >>> Volumes by Cylindrical Shells 1292 6.4 >>> Work 1293 6.5 >>> Average Value of a Function 1294 1295 7 >>> Techniques of Integration 1296 7.1 >>> Integration by Parts 1297 7.2 >>> Trigonometric Integrals 1298 7.3 >>> Trigonometric Substitution 1299 7.4 >>> Integration of Rational Functions by Partial Fractions 1300 7.5 >>> Strategy for Integration 1301 7.6 >>> Integration Using Tables and Computer Algebra Systems 1302 7.7 >>> Approximate Integration 1303 7.8 >>> Improper Integrals 1304 1305 8 >>> Further Applications of Integration 1306 8.1 >>> Arc Length 1307 8.2 >>> Area of a Surface of Revolution 1308 8.3 >>> Applications to Physics and Engineering 1309 8.4 >>> Applications to Economics and Biology 1310 8.5 >>> Probability 1311 1312 9 >>> Differential Equations 1313 9.1 >>> Modeling with Differential Equations 1314 9.2 >>> Direction Fields and Euler's Method 1315 9.3 >>> Separable Equations 1316 9.4 >>> Models for Population Growth 1317 9.5 >>> Linear Equations 1318 9.6 >>> Predator-Prey Systems 1319 1320 10 >>> Parametric Equations and Polar Coordinates 1321 10.1 >>> Curves Defined by Parametric Equations 1322 10.2 >>> Calculus with Parametric Curves 1323 10.3 >>> Polar Coordinates 1324 10.4 >>> Areas and Lengths in Polar Coordinates 1325 10.5 >>> Conic Sections 1326 10.6 >>> Conic Sections in Polar Coordinates 1327 1328 11 >>> Infinite Sequences and Series 1329 11.1 >>> Sequences 1330 11.2 >>> Series 1331 11.3 >>> The Integral Test and Estimates of Sum 1332 11.4 >>> The Comparison Tests 1333 11.5 >>> Alternating Series 1334 11.6 >>> Absolute Convergence and the Ratio and Root Tests 1335 11.7 >>> Strategy for Testing Series 1336 11.8 >>> Power Series 1337 11.9 >>> Representations of Functions as Power Series 1338 11.10 >>> Taylor and Maclaurin Series 1339 11.11 >>> Applications of Taylor Polynomials 1340 1341 12 >>> Vectors and the Geometry of Space 1342 12.1 >>> Three-Dimensional Coordinate Systems 1343 12.2 >>> Vectors 1344 12.3 >>> The Dot Product 1345 12.4 >>> The Cross Product 1346 12.5 >>> Equations of Lines and Planes 1347 12.6 >>> Cylinders and Quadric Surfaces 1348 1349 13 >>> Vector Functions 1350 13.1 >>> Vector Functions and Space Curves 1351 13.2 >>> Derivatives and Integrals of Vector Functions 1352 13.3 >>> Arc Length and Curvature 1353 13.4 >>> Motion in Space: Velocity and Acceleration 1354 1355 14 >>> Partial Derivatives 1356 14.1 >>> Functions of Several Variables 1357 14.2 >>> Limits and Continuity 1358 14.3 >>> Partial Derivatives 1359 14.4 >>> Tangent Planes and Linear Approximations 1360 14.5 >>> The Chain Rule 1361 14.6 >>> Directional Derivatives and the Gradient Vector 1362 14.7 >>> Maximum and Minimum Values 1363 14.8 >>> Lagrange Multipliers 1364 1365 15 >>> Multiple Integrals 1366 15.1 >>> Double Integrals over Rectangles 1367 15.2 >>> Iterated Integrals 1368 15.3 >>> Double Integrals over General Regions 1369 15.4 >>> Double Integrals in Polar Coordinates 1370 15.5 >>> Applications of Double Integrals 1371 15.6 >>> Triple Integrals 1372 15.7 >>> Triple Integrals in Cylindrical Coordinates 1373 15.8 >>> Triple Integrals in Spherical Coordinates 1374 15.9 >>> Change of Variables in Multiple Integrals 1375 1376 16 >>> Vector Calculus 1377 16.1 >>> Vector Fields 1378 16.2 >>> Line Integrals 1379 16.3 >>> The Fundamental Theorem for Line Integrals 1380 16.4 >>> Green's Theorem 1381 16.5 >>> Curl and Divergence 1382 16.6 >>> Parametric Surfaces and their Areas 1383 16.7 >>> Surface Integrals 1384 16.8 >>> Stokes' Theorem 1385 16.9 >>> The Divergence Theorem 1386 16.10 >>> Summary 1387 1388 17 >>> Second-Order Differential Equations 1389 17.1 >>> Second-Order Linear Equations 1390 17.2 >>> Nonhomogeneous Linear Equations 1391 17.3 >>> Applications of Second-Order Differential Equations 1392 17.4 >>> Series Solutions 1393 1394 18 >>> Appendix A: Numbers, Inequalities, and Absolute Values 1395 19 >>> Appendix B: Coordinate Geometry and Lines 1396 20 >>> Appendix C: Graphs of Second-Degree Equations 1397 21 >>> Appendix D: Trigonometry 1398 22 >>> Appendix E: Sigma Notation 1399 23 >>> Appendix F: Proofs of Theorems 1400 24 >>> Appendix G: The Logarithm Defined as an Integral 1401 25 >>> Appendix H: Complex Numbers 1402 26 >>> Appendix I: Answers to Odd-Numbered Exercises 1403 1404 TitleText('College Algebra') 1405 EditionText('3') 1406 AuthorText('Stewart, Redlin, Watson') 1407 1408 1 >>> Basic Algebra 1409 1.1 >>> What is Algebra? 1410 1.2 >>> Real Numbers 1411 1.3 >>> Exponentials and Radicals 1412 1.4 >>> Algebraic Equations 1413 1.5 >>> Fractional Expressions 1414 1.6 >>> Basic Equations 1415 2 >>> Coordinates and Graphs 1416 2.1 >>> The Coordinate Plane 1417 2.2 >>> Graphs of Equations 1418 2.3 >>> Graphing Calculators and Computers 1419 2.4 >>> Lines 1420 3 >>> Equations and Inequalities 1421 3.1 >>> Algebraic and Graphical Solutions of Equations 1422 3.2 >>> Modeling with Equations 1423 3.3 >>> Quadratic Equations 1424 3.4 >>> Complex Numbers 1425 3.5 >>> Other Equations 1426 3.6 >>> Linear Inequalities 1427 3.7 >>> Nonlinear Inequalities 1428 3.8 >>> Absolute Value 1429 4 >>> Functions 1430 4.1 >>> What is a Function? 1431 4.2 >>> Graphs of Functions 1432 4.3 >>> Applied Functions: Variation 1433 4.4 >>> Average Rate of Change: Increasing and Decreasing Functions 1434 4.5 >>> Transformations of Functions 1435 4.6 >>> Extreme Values of Functions 1436 4.7 >>> Combining Functions 1437 4.8 >>> One-to-One Functions and Their Inverses 1438 5 >>> Polynomial and Rational Functions 1439 5.1 >>> Polynomial Functions and Their Graphs 1440 5.2 >>> Dividing Polynomials 1441 5.3 >>> Real Zeros of Polynomials 1442 5.4 >>> The Fundamental Theorem of Algebra 1443 5.5 >>> Rational Functions 1444 6 >>> Exponential and Logarithmic Functions 1445 6.1 >>> Exponential Functions 1446 6.2 >>> The Natural Exponential Function 1447 6.3 >>> Logistic Functions 1448 6.4 >>> Laws of Logarithms 1449 6.5 >>> Exponential and Logarithmic Equations 1450 6.6 >>> Applications of Exponential and Logarithmic Functions 1451 7 >>> Systems of Equations and Inequalities 1452 7.1 >>> Systems of Equations 1453 7.2 >>> Pairs of Lines 1454 7.3 >>> Systems of Linear Equations 1455 7.4 >>> The Algebra of Matrices 1456 7.5 >>> Inverses of Matrices and Matrix Equations 1457 7.6 >>> Determinants and Cramer's Rule 1458 7.7 >>> Systems of Inequalities 1459 7.8 >>> Partial Fractions 1460 8 >>> Conic Sections 1461 8.1 >>> Parabolas 1462 8.2 >>> Ellipses 1463 8.3 >>> Hyperbolas 1464 8.4 >>> Shifted Conics 1465 9 >>> Sequences and Series 1466 9.1 >>> Sequences and Summation Notation 1467 9.2 >>> Arithmetic Sequences 1468 9.3 >>> Geometric Sequences 1469 9.4 >>> Annuities and Installment Buying 1470 9.5 >>> Mathematical Induction 1471 9.6 >>> The Binomial Theorem 1472 10 >>> Counting and Probability 1473 10.1 >>> Counting Principles 1474 10.2 >>> Permutations and Combinations 1475 10.3 >>> Probability 1476 10.4 >>> Expected Value 1477 1478 TitleText('Precalculus') 1479 EditionText('3') 1480 AuthorText('Stewart, Redlin, Watson') 1481 1482 1 >>> Fundamentals 1483 1.1 >>> Real Numbers 1484 1.2 >>> Exponents and Radicals 1485 1.3 >>> Algebraic Expressions 1486 1.4 >>> Fractional Expressions 1487 1.5 >>> Equations 1488 1.6 >>> Problem Solving with Equations 1489 1.7 >>> Inequalities 1490 1.8 >>> Coordinate Geometry 1491 1.9 >>> Graphing Calculators and Computers 1492 1.10 >>> Lines 1493 1494 2 >>> Functions 1495 2.1 >>> What is a Function? 1496 2.2 >>> Graphs of Functions 1497 2.3 >>> Applied Functions 1498 2.4 >>> Transformations of Functions 1499 2.5 >>> Extreme Values of Functions 1500 2.6 >>> Combining Functions 1501 2.7 >>> One-to-One Functions and Their Inverses 1502 1503 3 >>> Polynomials and Rational Functions 1504 3.1 >>> Polynomial Functions and Their Graphs 1505 3.2 >>> Real Zeros of Polynomials 1506 3.3 >>> Complex Numbers 1507 3.4 >>> Complex Roots and The Fundamental Theorem of Algebra 1508 3.5 >>> Rational Functions 1509 4 >>> Exponential and Logarithmic Functions 1510 4.1 >>> Exponential Functions 1511 4.2 >>> The Natural Exponential Function 1512 4.3 >>> Logarithmic Functions 1513 4.4 >>> Laws of Logarithms 1514 4.5 >>> Exponential and Logarithmic Equations 1515 4.6 >>> Applications of Exponential and Logarithmic Equations 1516 5 >>> Trigonometric Functions 1517 5.1 >>> The Unit Circle 1518 5.2 >>> Trigonometric Functions of Real Numbers 1519 5.3 >>> Trigonometric Graphs 1520 5.4 >>> More Trigonometric Graphs 1521 6 >>> Trigonometric Functions of Angles 1522 6.1 >>> Angle Measure 1523 6.2 >>> Trigonometry of Right Triangles 1524 6.3 >>> Trigonometric Functions of Angles 1525 6.4 >>> The Law of Sines 1526 6.5 >>> The Law of Cosines 1527 7 >>> Analytic Trigonometry 1528 7.1 >>> Trigonometric Identities 1529 7.2 >>> Addition and Subtraction Formulas 1530 7.3 >>> Double-Angle, Half-Angle, and Product-Sum Formulas 1531 7.4 >>> Inverse Trigonometric Functions 1532 7.5 >>> Trigonometric Equations 1533 7.6 >>> Trigonometric Form of Complex Numbers; DeMoivre's Theorem 1534 7.7 >>> Vectors 1535 8 >>> Systems of Equations and Inequalities 1536 8.1 >>> Systems of Equations 1537 8.2 >>> Pairs of Lines 1538 8.3 >>> Systems of Linear Equations 1539 8.4 >>> The Algebra of Matrices 1540 8.5 >>> Inverses of Matrices and Matrix Equations 1541 8.6 >>> Determinants and Cramer's Rule 1542 8.7 >>> Systems of Inequalities 1543 8.8 >>> Partial Fractions 1544 9 >>> Topics in Analytic Geometry 1545 9.1 >>> Parabolas 1546 9.2 >>> Ellipses 1547 9.3 >>> Hyperbolas 1548 9.4 >>> Shifted Conics 1549 9.5 >>> Rotation of Axes 1550 9.6 >>> Polar Coordinates 1551 9.7 >>> Polar Equations of Conics 1552 9.8 >>> Parametric Equations 1553 10 >>> Sequences and Series 1554 10.1 >>> Sequences and Summation Notation 1555 10.2 >>> Arithmetic Sequences 1556 10.3 >>> Geometric Sequences 1557 10.4 >>> Annuities and Installment Buying 1558 10.5 >>> Mathematical Induction 1559 10.6 >>> The Binomial Theorem 1560 11 >>> Counting and Probability 1561 11.1 >>> Counting Principles 1562 11.2 >>> Permutations and Combinations 1563 11.3 >>> Probability 1564 11.4 >>> Expected Value 1565 1566 1567 TitleText('Functions Modeling Change') 1568 EditionText('3') 1569 AuthorText('Connally') 1570 1571 1 >>> Linear Functions and Change 1572 1.1 >>> Functions and Function Notation 1573 1.2 >>> Rate of Change 1574 1.3 >>> Linear Functions 1575 1.4 >>> Formulas for Linear Functions 1576 1.5 >>> Geometric Properties of Linear Functions 1577 1.6 >>> Fitting Linear Functions to Data 1578 2 >>> Functions 1579 2.1 >>> Input and Output 1580 2.2 >>> Domain and Range 1581 2.3 >>> Piecewise Defined Functions 1582 2.4 >>> Composite and Inverse Functions 1583 2.5 >>> Concavity 1584 2.6 >>> Quadratic Functions 1585 3 >>> Exponential Functions 1586 3.1 >>> Introduction to the Family of Exponential Functions 1587 3.2 >>> Comparing Exponential and Linear Functions 1588 3.3 >>> Graphs of Exponential Functions 1589 3.4 >>> Continuous Growth and the Number e 1590 3.5 >>> Compound Interest 1591 4 >>> Logarithmic Functions 1592 4.1 >>> Logarithms and their Properties 1593 4.2 >>> Logarithms and Exponential Models 1594 4.3 >>> The Logarithmic Function 1595 4.4 >>> Logarithmic Scales 1596 5 >>> Transformations of Functions and their Graphs 1597 5.1 >>> Vertical and Horizontal Shifts 1598 5.2 >>> Reflections and Symmetry 1599 5.3 >>> Vertical Stretches and Compressions 1600 5.4 >>> Horizontal Stretches and Compressions 1601 5.5 >>> The Family of Quadratic Functions 1602 6 >>> Trigonometric Functions 1603 6.1 >>> Introduction to Periodic Functions 1604 6.2 >>> The Sine and Cosine Functions 1605 6.3 >>> Radians 1606 6.4 >>> Graphs of the Sine and Cosine 1607 6.5 >>> Sinusoidal Functions 1608 6.6 >>> Other Trigonometric Functions 1609 6.7 >>> Inverse Trigonometric Functions 1610 7 >>> Trigonometry 1611 7.1 >>> General Triangles: Laws of Sines and Cosines 1612 7.2 >>> Trigonometric Identities 1613 7.3 >>> Sum and Difference Formulas for Sine and Cosine 1614 7.4 >>> Trigonometric Models 1615 7.5 >>> Polar Coordinates 1616 7.6 >>> Complex Numbers and Polar Coordinates 1617 8 >>> Compositions, Inverses and Combinations of Functions 1618 8.1 >>> Composition of Functions 1619 8.2 >>> Inverse Functions 1620 8.3 >>> Combinations of Functions 1621 9 >>> Polynomial and Rational Functions 1622 9.1 >>> Power Functions 1623 9.2 >>> Polynomial Functions 1624 9.3 >>> The Short-Run Behavior of Polynomials 1625 9.4 >>> Rational Functions 1626 9.5 >>> The Short-Run Behavior of Rational Functions 1627 9.6 >>> Comparing Power, Exponential and Log Functions 1628 9.7 >>> Fitting Exponentials and Polynomials to Data 1629 10 >>> Vector and Matrices 1630 10.1 >>> Vectors 1631 10.2 >>> The Components of a Vector 1632 10.3 >>> Application of Vectors 1633 10.4 >>> The Dot Product 1634 10.5 >>> Matrices 1635 11 >>> Sequences and Series 1636 11.1 >>> Sequences 1637 11.2 >>> Defining Functions Using Sums: Arithmetic Series 1638 11.3 >>> Finite Geometric Series 1639 11.4 Infinite Geometric Series 1640 12 >>> Parametric Equations and Conic Sections 1641 12.1 >>> Parametric Equations 1642 12.2 >>> Implicitly Defined Curves and Circles 1643 12.3 >>> Ellipses 1644 12.4 >>> Hyperbolas 1645 12.5 >>> Geometric Properties of Conic Sections 1646 12.6 >>> Hyperbolic Functions 1647 1648 1649 TitleText('Calculus') 1650 EditionText('4') 1651 AuthorText('Hughes-Hallett') 1652 1653 1 >>> A Library of Functions 1654 1.1 >>> Functions and Change 1655 1.2 >>> Exponential Functions 1656 1.3 >>> New Functions from Old 1657 1.4 >>> Logarithmic Functions 1658 1.5 >>> Trigonometric Functions 1659 1.6 >>> Powers, Polynomials, and Rational Functions 1660 1.7 >>> Introduction to Continuity 1661 1.8 >>> Limits 1662 2 >>> Key Concept: The Derivative 1663 2.1 >>> How do we measure speed? 1664 2.2 >>> The Derivative at a Point 1665 2.3 >>> The Derivative Function 1666 2.4 >>> Interpretations of the Derivative 1667 2.5 >>> The Second Derivative 1668 2.6 >>> Differentiability 1669 3 >>> Shortcuts to Differentiation 1670 3.1 >>> Powers and Polynomials 1671 3.2 >>> The Exponential Function 1672 3.3 >>> The Product and Quotient Rules 1673 3.4 >>> The Chain Rule 1674 3.5 >>> The Trigonometric Functions 1675 3.6 >>> The Chain Rule and Inverse Functions 1676 3.7 >>> Implicit Functions 1677 3.8 >>> Hyperbolic Functions 1678 3.9 >>> Linear Approximation and the Derivative 1679 3.10 >>> Theorems About Differentiable Functions 1680 4 >>> Using the Derivative 1681 4.1 >>> Using First and Second Derivatives 1682 4.2 >>> Families of Curves 1683 4.3 >>> Optimization 1684 4.4 >>> Applications to Marginality 1685 4.5 >>> Optimization and Modeling 1686 4.6 >>> Rates and Related Rates 1687 4.7 >>> L'Hopital's Rule, Growth, and Dominance 1688 4.8 >>> Parametric Equations 1689 5 >>> Key Concept: The Definite Integral 1690 5.1 >>> How do we measure distance traveled? 1691 5.2 >>> The Definite Integral 1692 5.3 >>> The Fundamental Theorem and Interpretations 1693 5.4 >>> Theorems About Definite Integrals 1694 6 >>> Constructing Antiderivatives 1695 6.1 >>> Antiderivatives Graphically and Numerically 1696 6.2 >>> Constructing Antiderivatives Analytically 1697 6.3 >>> Differential Equations 1698 6.4 >>> Second Fundamental Theorem of Calculus 1699 6.5 >>> The Equations of Motion 1700 7 >>> Integration 1701 7.1 >>> Integration by Substitution 1702 7.2 >>> Integration by Parts 1703 7.3 >>> Tables of Integrals 1704 7.4 >>> Algebraic Identities and Trigonometric Substitutions 1705 7.5 >>> Approximating Definite Integrals 1706 7.6 >>> Approximation Errors an Simpson's Rule 1707 7.7 >>> Improper Integrals 1708 7.8 >>> Comparison of Improper Integrals 1709 8 >>> Using the Definite Integral 1710 8.1 >>> Areas and Volumes 1711 8.2 >>> Applications to Geometry 1712 8.3 >>> Area and Arc Length in Polar Coordinates 1713 8.4 >>> Density and Center of Mass 1714 8.5 >>> Applications to Physics 1715 8.6 >>> Applications to Economics 1716 8.7 >>> Distribution Functions 1717 8.8 >>> Probability, Mean, and Median 1718 9 >>> Sequences and Series 1719 9.1 >>> Sequences 1720 9.2 >>> Geometric Series 1721 9.3 >>> Convergence of Series 1722 9.4 >>> Tests for Convergence 1723 9.5 >>> Power Series and Interval of Convergence 1724 10 >>> Approximating Functions Using Series 1725 10.1 >>> Taylor Polynomials 1726 10.2 >>> Taylor Series 1727 10.3 >>> Finding and Using Taylor Series 1728 10.4 >>> The Error in Taylor Polynomial Approximations 1729 10.5 >>> Fourier Series 1730 11 >>> Differential Equations 1731 11.1 >>> What is a differential equation? 1732 11.2 >>> Slope Fields 1733 11.3 >>> Euler's Method 1734 11.4 >>> Separation of Variables 1735 11.5 >>> Growth and Decay 1736 11.6 >>> Applications and Modeling 1737 11.7 >>> Models of Population Growth 1738 11.8 >>> Systems of Differential Equations 1739 11.9 >>> Analyzing the Phase Plane 1740 11.10 >>> Second-Order Differential Equations: Oscillations 1741 11.11 >>> Linear Second-Order Differential Equations 1742 12 >>> Functions of Several Variables 1743 12.1 >>> Functions of Two Variables 1744 12.2 >>> Graphs of Functions of Two Variables 1745 12.3 >>> Control Diagrams 1746 12.4 >>> Linear Functions 1747 12.5 >>> Functions of Three Variables 1748 12.6 >>> Limits and Continuity 1749 13 >>> A Fundamental Tool: Vectors 1750 13.1 >>> Displacement Vectors 1751 13.2 >>> Vectors in General 1752 13.3 >>> The Dot Product 1753 13.4 >>> The Cross Product 1754 14 >>> Differentiating Functions of Several Variables 1755 14.1 >>> The Partial Derivative 1756 14.2 >>> Computing Partial Derivatives Algebraically 1757 14.3 >>> Local Linearity and the Differential 1758 14.4 >>> Gradients and Directional Derivatives in the Plane 1759 14.5 >>> Gradients and Directional Derivatives in Space 1760 14.6 >>> The Chain Rule 1761 14.7 >>> Second-Order Partial Derivatives 1762 14.8 >>> Differentiability 1763 15 >>> Optimization: Local and Global Extrema 1764 15.1 >>> Local Extrema 1765 15.2 >>> Optimization 1766 15.3 >>> Constrained Optimization: Lagrange Multipliers 1767 16 >>> Integrating Functions of Several Variables 1768 16.1 >>> The Definite Integral of a Function of Two Variables 1769 16.2 >>> Iterated Integrals 1770 16.3 >>> Triple Integrals 1771 16.4 >>> Double Integrals in Polar Coordinates 1772 16.5 >>> Integrals in Cylindrical and Spherical Coordinates 1773 16.6 >>> Applications of Integration to Probability 1774 16.7 >>> Change of Variables in Multiple Integral 1775 17 >>> Parameterization and Vector Fields 1776 17.1 >>> Parameterized Curves 1777 17.2 >>> Motion, Velocity, and Acceleration 1778 17.3 >>> Vector Fields 1779 17.4 >>> The Flow of a Vector Field 1780 17.5 >>> Parameterized Surfaces 1781 18 >>> Line Integrals 1782 18.1 >>> The Idea of a Line Integral 1783 18.2 >>> Computing Line Integrals Over Parameterized Curves 1784 18.3 >>> Gradient Fields and Path-Independent Fields 1785 18.4 >>> Path-Independent Vector Fields and Green's Theorem 1786 19 >>> Flux Integrals 1787 19.1 >>> The Idea of a Flux Integral 1788 19.2 >>> Flux Integrals for Graphs, Cylinders, and Spheres 1789 19.3 >>> Flux Integrals over Parameterized Surfaces 1790 20 >>> Calculus of Vector Fields 1791 20.1 >>> The Divergence of a Vector Field 1792 20.2 >>> The Divergence Theorem 1793 20.3 >>> The Curl of a Vector Field 1794 20.4 >>> Stokes' Theorem 1795 20.5 >>> The Three Fundamental Theorems 1796 1797 TitleText('Calculus') 1798 EditionText('5') 1799 AuthorText('Hughes-Hallett') 1800 1801 1 >>> A Library of Functions 1802 1.1 >>> Functions and Change 1803 1.2 >>> Exponential Functions 1804 1.3 >>> New Functions From Old 1805 1.4 >>> Logarithmic Functions 1806 1.5 >>> Trigonometric Functions 1807 1.6 >>> Powers, Polynomials and Rational Functions 1808 1.7 >>> Introduction to Continuity 1809 1.8 >>> Limits 1810 2 >>> Key Concept: The Derivative 1811 2.1 >>> How Do We Measure Speed 1812 2.2 >>> The Derivative at a Point 1813 2.3 >>> The Derivative Function 1814 2.4 >>> Interpretations of the Derivative 1815 2.5 >>> The Second Derivative 1816 2.6 >>> Differentiability 1817 3 >>> Short-Cuts to Differentiation 1818 3.1 >>> Powers and Polynomials 1819 3.2 >>> The Exponential Function 1820 3.3 >>> The Product and Quotient Rules 1821 3.4 >>> The Chain Rule 1822 3.5 >>> The Trigonometric Functions 1823 3.6 >>> The Chain Rule and Inverse Functions 1824 3.7 >>> Implicit Functions 1825 3.8 >>> Hyperbolic Functions 1826 3.9 >>> Linear Approximation and the Derivative 1827 3.10 >>> Theorems About Differentiable Functions 1828 4 >>> Using the Derivative 1829 4.1 >>> Using First and Second Derivatives 1830 4.2 >>> Optimization 1831 4.3 >>> Families of Functions 1832 4.4 >>> Optimization, Geometry and Modeling 1833 4.5 >>> Applications to Marginality 1834 4.6 >>> Rates and Related Rates 1835 4.7 >>> L'Hopital's Rule, Growth and Dominance 1836 4.8 >>> Parametric Equations 1837 5 >>> Key Concept: The Definite Integral 1838 5.1 >>> How Do We Measure Distance Traveled 1839 5.2 >>> The Definite Integral 1840 5.3 >>> The Fundamental Theorem and Interpretations 1841 5.4 >>> Theorems about Definite Integrals 1842 6 >>> Constructing Antiderivatives 1843 6.1 >>> Antiderivatives Graphically and Numerically 1844 6.2 >>> Constructing Antiderivatives Analytically 1845 6.3 >>> Differential Equations 1846 6.4 >>> The Second Fundamental Theorem of Calculus 1847 6.5 >>> The Equations of Motion 1848 7 >>> Integration 1849 7.1 >>> Integration by Substitution 1850 7.2 >>> Integration by Parts 1851 7.3 >>> Tables of Integrals 1852 7.4 >>> Algebraic Identities and Trigonometric Substitutions 1853 7.5 >>> Approximating Definite Integrals 1854 7.6 >>> Approximation Errors and Simpson's Rule 1855 7.7 >>> Improper Integrals 1856 7.8 >>> Comparison of Improper Integrals 1857 8 >>> Using the Definite Integral 1858 8.1 >>> Areas and Volumes 1859 8.2 >>> Applications to Geometry 1860 8.3 >>> Area and Arc Length in Polar Coordinates 1861 8.4 >>> Density and Center of Mass 1862 8.5 >>> Applications to Physics 1863 8.6 >>> Applications to Economics 1864 8.7 >>> Distribution Functions 1865 8.8 >>> Probability, Mean and Median 1866 9 >>> Sequences and Series 1867 9.1 >>> Sequences 1868 9.2 >>> Geometric Series 1869 9.3 >>> Convergence of Series 1870 9.4 >>> Tests for Convergence 1871 9.5 >>> Power Series and Interval of Convergence 1872 10 >>> Approximating Functions Using Series 1873 10.1 >>> Taylor Polynomials 1874 10.2 >>> Taylor Series 1875 10.3 >>> Finding and Using Taylor Series 1876 10.4 >>> The Error in Taylor Polynomial Approximations 1877 10.5 >>> Fourier Series 1878 11 >>> Differential Equations 1879 11.1 >>> What is a Differential Equation 1880 11.2 >>> Slope Fields 1881 11.3 >>> Euler's Method 1882 11.4 >>> Separation of Variables 1883 11.5 >>> Growth and Decay 1884 11.6 >>> Applications and Modeling 1885 11.7 >>> The Logistic Model 1886 11.8 >>> Systems of Differential Equations 1887 11.9 >>> Analyzing the Phase Plane 1888 11.10 >>> Second-Order Differential Equations: Oscillations 1889 11.11 >>> Linear Second-Order Differential Equations 1890 12 >>> Functions of Several Variables 1891 12.1 >>> Functions of Two Variables 1892 12.2 >>> Graphs of Functions of Two Variables 1893 12.3 >>> Control Diagrams 1894 12.4 >>> Linear Functions 1895 12.5 >>> Functions of Three Variables 1896 12.6 >>> Limits and Continuity 1897 13 >>> A Fundamental Tool: Vectors 1898 13.1 >>> Displacement Vectors 1899 13.2 >>> Vectors in General 1900 13.3 >>> The Dot Product 1901 13.4 >>> The Cross Product 1902 14 >>> Differentiating Functions of Several Variables 1903 14.1 >>> The Partial Derivative 1904 14.2 >>> Computing Partial Derivatives Algebraically 1905 14.3 >>> Local Linearity and the Differential 1906 14.4 >>> Gradients and Directional Derivatives in the Plane 1907 14.5 >>> Gradients and Directional Derivatives in Space 1908 14.6 >>> The Chain Rule 1909 14.7 >>> Second-Order Partial Derivatives 1910 14.8 >>> Differentiability 1911 15 >>> Optimization: Local and Global Extrema 1912 15.1 >>> Local Extrema 1913 15.2 >>> Optimization 1914 15.3 >>> Constrained Optimization: Lagrange Multipliers 1915 16 >>> Integrating Functions of Several Variables 1916 16.1 >>> The Definite Integral of a Function of Two Variables 1917 16.2 >>> Iterated Integrals 1918 16.3 >>> Triple Integrals 1919 16.4 >>> Double Integrals in Polar Coordinates 1920 16.5 >>> Integrals in Cylindrical and Spherical Coordinates 1921 16.6 >>> Applications of Integration to Probability 1922 16.7 >>> Change of Variables in Multiple Integral 1923 17 >>> Parameterization and Vector Fields 1924 17.1 >>> Parameterized Curves 1925 17.2 >>> Motion, Velocity, and Acceleration 1926 17.3 >>> Vector Fields 1927 17.4 >>> The Flow of a Vector Field 1928 17.5 >>> Parameterized Surfaces 1929 18 >>> Line Integrals 1930 18.1 >>> The Idea of a Line Integral 1931 18.2 >>> Computing Line Integrals Over Parameterized Curves 1932 18.3 >>> Gradient Fields and Path-Independent Fields 1933 18.4 >>> Path-Independent Vector Fields and Green's Theorem 1934 19 >>> Flux Integrals 1935 19.1 >>> The Idea of a Flux Integral 1936 19.2 >>> Flux Integrals for Graphs, Cylinders, and Spheres 1937 19.3 >>> Flux Integrals over Parameterized Surfaces 1938 20 >>> Calculus of Vector Fields 1939 20.1 >>> The Divergence of a Vector Field 1940 20.2 >>> The Divergence Theorem 1941 20.3 >>> The Curl of a Vector Field 1942 20.4 >>> Stokes' Theorem 1943 20.5 >>> The Three Fundamental Theorems 1944 1945 TitleText('Calculus: Early Transcendentals') 1946 EditionText('1') 1947 AuthorText('Rogawski') 1948 1949 1 >>> Precalculus Review 1950 1.1 >>> Real Numbers, Functions, and Graphs 1951 1.2 >>> Linear and Quadratic Functions 1952 1.3 >>> The Basic Classes of Functions 1953 1.4 >>> Trigonometric Functions 1954 1.5 >>> Inverse Functions 1955 1.6 >>> Exponential and Logarithmic Functions 1956 1.7 >>> Technology: Calculators and Computers 1957 2 >>> Limits 1958 2.1 >>> Limits, Rates of Change, and Tangent Lines 1959 2.2 >>> Limits: A Numerical and Graphical Approach 1960 2.3 >>> Basic Limit Laws 1961 2.4 >>> Limits and Continuity 1962 2.5 >>> Evaluating Limits Algebraically 1963 2.6 >>> Trigonometric Limits 1964 2.7 >>> Intermediate Value Theorem 1965 2.8 >>> The Formal Definition of a Limit 1966 3 >>> Differentiation 1967 3.1 >>> Definition of the Derivative 1968 3.2 >>> The Derivative as a Function 1969 3.3 >>> Product and Quotient Rules 1970 3.4 >>> Rates of Change 1971 3.5 >>> Higher Derivatives 1972 3.6 >>> Trigonometric Functions 1973 3.7 >>> The Chain Rule 1974 3.8 >>> Implicit Differentiation 1975 3.9 >>> Derivatives of Inverse Functions 1976 3.10 >>> Derivatives of General Exponential and Logarithmic Functions 1977 3.11 >>> Related Rates 1978 4 >>> Applications of the Derivative 1979 4.1 >>> Linear Approximation and Applications 1980 4.2 >>> Extreme Values 1981 4.3 >>> The Mean Value Theorem and Monotonicity 1982 4.4 >>> The Shape of a Graph 1983 4.5 >>> Graph Sketching and Asymptotes 1984 4.6 >>> Applied Optimization 1985 4.7 >>> L'Hopital's Rule 1986 4.8 >>> Newton's Method 1987 4.9 >>> Antiderivatives 1988 5 >>> The Integral 1989 5.1 >>> Approximating and Computing Area 1990 5.2 >>> The Definite Integral 1991 5.3 >>> The Fundamental Theorem of Calculus, Part I 1992 5.4 >>> The Fundamental Theorem of Calculus, Part II 1993 5.5 >>> Net or Total Change as the Integral of a Rate 1994 5.6 >>> Substitution Method 1995 5.7 >>> Further Transcendental Functions 1996 5.8 >>> Exponential Growth and Decay 1997 6 >>> Applications of the Integral 1998 6.1 >>> Area Between Two Curves 1999 6.2 >>> Setting Up Integrals: Volumes, Density, Average Value 2000 6.3 >>> Volumes of Revolution 2001 6.4 >>> The Method of Cylindrical Shells 2002 6.5 >>> Work and Energy 2003 7 >>> Techniques of Integration 2004 7.1 >>> Numerical Integration 2005 7.2 >>> Integration by Parts 2006 7.3 >>> Trigonometric Integrals 2007 7.4 >>> Trigonometric Substitution 2008 7.5 >>> Integrals of Hyperbolic and Inverse Hyperbolic Functions 2009 7.6 >>> The Method of Partial Fractions 2010 7.7 >>> Improper Integrals 2011 8 >>> Further Applications of the Integral and Taylor Polynomials 2012 8.1 >>> Arc Length and Surface Area 2013 8.2 >>> Fluid Pressure and Force 2014 8.3 >>> Center of Mass 2015 8.4 >>> Taylor Polynomials 2016 9 >>> Introduction to Differential Equations 2017 9.1 >>> Solving Differential Equations 2018 9.2 >>> Models Involving y'=k(y-b) 2019 9.3 >>> Graphical and Numerical Methods 2020 9.4 >>> The Logistic Equation 2021 9.5 >>> First-Order Linear Equations 2022 10 >>> Infinite Series 2023 10.1 >>> Sequences 2024 10.2 >>> Summing an Infinite Series 2025 10.3 >>> Convergence of Series with Positive Terms 2026 10.4 >>> Absolute and Conditional Convergence 2027 10.5 >>> The Ratio and Root Tests 2028 10.6 >>> Power Series 2029 10.7 >>> Taylor Series 2030 11 >>> Parametric Equations, Polar Coordinates, and Conic Sections 2031 11.1 >>> Parametric Equations 2032 11.2 >>> Arc Length and Speed 2033 11.3 >>> Polar Coordinates 2034 11.4 >>> Area and Arc Length in Polar Coordinates 2035 11.5 >>> Conic Sections 2036 12 >>> Vector Geometry 2037 12.1 >>> Vectors in the Plane 2038 12.2 >>> Vectors in Three Dimensions 2039 12.3 >>> Dot Product and the Angle Between Two Vectors 2040 12.4 >>> The Cross Product 2041 12.5 >>> Planes in Three-Space 2042 12.6 >>> A Survey of Quadric Surfaces 2043 12.7 >>> Cylindrical and Spherical Coordinates 2044 13 >>> Calculus of Vector-Valued Functions 2045 13.1 >>> Vector-Valued Functions 2046 13.2 >>> Calculus of Vector-Valued Functions 2047 13.3 >>> Arc Length and Speed 2048 13.4 >>> Curvature 2049 13.5 >>> Motion in Three-Space 2050 13.6 >>> Planetary Motion According to Kepler and Newton 2051 14 >>> Differentiation in Several Variables 2052 14.1 >>> Functions in Two or More Variables 2053 14.2 >>> Limits and Continuity in Several Variables 2054 14.3 >>> Partial Derivatives 2055 14.4 >>> Differentiability, Linear Approximation, and Tangent Planes 2056 14.5 >>> The Gradient and Directional Derivatives 2057 14.6 >>> The Chain Rule 2058 14.7 >>> Optimization in Several Variables 2059 14.8 >>> Lagrange Multipliers: Optimizing with a Constraint 2060 15 >>> Multiple Integration 2061 15.1 >>> Integrals in Several Variables 2062 15.2 >>> Double Integrals over More General Regions 2063 15.3 >>> Triple Integrals 2064 15.4 >>> Integration in Polar, Cylindrical, and Spherical Coordinates 2065 15.5 >>> Change of Variables 2066 16 >>> Line and Surface Integrals 2067 16.1 >>> Vector Fields 2068 16.2 >>> Line Integrals 2069 16.3 >>> Conservative Vector Fields 2070 16.4 >>> Parametrized Surfaces and Surface Integrals 2071 16.5 >>> Integrals of Vector Fields 2072 17 >>> Fundamental Theorems of Vector Analysis 2073 17.1 >>> Green's Theorem 2074 17.2 >>> Stokes' Theorem 2075 17.3 >>> Divergence Theorem
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